Biblical Hebrew Forum

["K Randolph" <kwrandolph AT gmail.com>]

Peter:

I'm having an intuitive reaction that something doesn't seem right
here. I don't know enough to be able to tell what is wrong, but if the
formula is correct, it should not be giving the obviously incorrect
response for the resh.

I sent a copy of the spreadsheet with some explanatory info. to a
friend who has a PhD in statistics, but he hasn't responded yet.

Karl W. Randolph.

On 1/19/07, Peter Kirk <peter AT qaya.org> wrote:
> The formula for H(1,A) etc is as given in my previous post: (1/2)N^2 *
> p(1,A)^2 * sum of (p(2,B)^2) column * sum of (p(3,C)^2) column.
>
> I noted also that for resh the estimated homonym probability is so high,
> in fact nearly one in three, that the assumptions I was making break
> down. My first estimate for the probable number of homonyms for each
> root is (1/2)N^2 * (p(ABC))^2, or (to simplify) (Np)^2/2. But in fact
> there are higher order terms here, to adjust for cases for three or more
> homonyms, and I think the full formula comes to something like:
>
> (Np)^2/2 - (Np)^3/6 + (Np)^4/24 - ...
>
> Now if for a particular root the first estimate is 1/2, that implies
> that (Np) = 1, and so the second term in the series is 1/6, the third is
> 1/24 etc etc., and the sum is just above 1/3. In fact for the root
> nun-vav-resh (one of the most probable), p(ABC) =
> (137/1615)*(175/1615)*(210/1615) = 0.001195, and (Np) = 1.93. With a
> value of (Np) this high my approximations break down completely. As this
> kind of breakdown is most common with resh and medial vav, and as the
> expected effect is that the estimated number of homonyms should be
> significantly reduced, it is not surprising that for vav and resh the
> estimates proved to be significantly higher than expected.
>
> What all of this shows me is that the observed distribution of homonyms
> is very close to what would be expected from a random distribution of
> verbs. That tells us something about how the roots are distributed. It
> also, it seems to me, tells me that the people who detected homonyms
> among these verbs are on the right track, for they are consistently
> detecting the statistically expected number of homonyms.
>
> PS Sorry if we are boring others on the list with this.
>
> --
> Peter Kirk
> E-mail:  peter AT qaya.org
> Blog:    http://speakertruth.blogspot.com/
> Website: http://www.qaya.org/